Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

The role of animal nutrition in designing optimal foods of animal origin as reviewed by the COST Action Feed for Health (FA0802)

This review provides an overview of the main scientific outputs of a network (Action) supported by the European Cooperation in Science and Technology (COST) in the field of animal science, namely the COST Action Feed for Health (FA0802). The main aims of the COST Action Feed for Health (FA0802) were: to develop an integrated and collaborative network of research groups that focuses on the roles of feed and animal nutrition in improving animal wellbeing and also the quality, safety and wholesomeness of human foods of animal origin; to examine the consumer concerns and perceptions as regards livestock production systems. The COST Action Feed for Health has addressed these scientific topics during the last four years. From a practical point of view three main scientific fields of achievement can be identified: feed and animal nutrition; food of animal origin quality and functionality and consumers’ perceptions. Finally, the present paper has the scope to provide new ideas and solutions to a range of issues associated with the modern livestock production system.

Thermal and visual performance of real and theoretical thermochromic glazing solutions for office buildings

Thermochromic windows are able to modulate their transmittance in both the visible and the near-infrared field as a function of their temperature. As a consequence, they allow to control the solar gains in summer, thus reducing the energy needs for space cooling. However, they may also yield a reduction in the daylight availability, which results in the energy consumption for indoor artificial lighting being increased. This paper investigates, by means of dynamic simulations, the application of thermochromic windows to an existing office building in terms of energy savings on an annual basis, while also focusing on the effects in terms of daylighting and thermal comfort. In particular, due attention is paid to daylight availability, described through illuminance maps and by the calculation of the daylight factor, which in several countries is subject thresholds. The study considers both a commercially available thermochromic pane and a series of theoretical thermochromic glazing. The expected performance is compared to static clear and reflective insulating glass units. The simulations are repeated in different climatic conditions, showing that the overall energy savings compared to clear glazing can range from around 5% for cold climates to around 20% in warm climates, while not compromising daylight availability. Moreover the role played by the transition temperature of the pane is examined, pointing out an optimal transition temperatures that is irrespective of the climatic conditions.

A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

How does the use of different road networks effect the optimal location of facilities in rural areas?

The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure. Distance measure can vary if the accuracy of the road network varies. The rst aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to nd an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using dierent algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with an asymmetrically distributed population, Dalecarlia. The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is optimized for. It is also shown that the simulated annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better location solutions.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Efficient heuristic algorithm used for optimal capacitor placement in distribution systems

An efficient heuristic algorithm is presented in this work in order to solve the optimal capacitor placement problem in radial distribution systems. The proposal uses the solution from the mathematical model after relaxing the integrality of the discrete variables as a strategy to identify the most attractive bus to add capacitors to each step of the heuristic algorithm. The relaxed mathematical model is a nonlinear programming problem and is solved using a specialized interior point method, The algorithm still incorporates an additional strategy of local search that enables the finding of a group of quality solutions after small alterations in the optimization strategy. Proposed solution methodology has been implemented and tested in known electric systems getting a satisfactory outcome compared with metaheuristic methods.The tests carried out in electric systems known in specialized literature reveal the satisfactory outcome of the proposed algorithm compared with metaheuristic methods. (C) 2009 Elsevier Ltd. All rights reserved.

An improved tabu-based vector optimal algorithm for design optimizations of electromagnetic devices

This paper introduces an improved tabu-based vector optimal algorithm for multiobjective optimal designs of electromagnetic devices. The improvements include a division of the entire search process, a new method for fitness assignment, a novel scheme for the generation and selection of neighborhood solutions, and so forth. Numerical results on a mathematical function and an engineering multiobjective design problem demonstrate that the proposed method can produce virtually the exact Pareto front, in both parameter and objective spaces, even though the iteration number used by it is only about 70% of that required by its ancestor.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Optimal capacitor placement in radial distribution networks

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (Non Polynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

TIME-OPTIMAL GEOMAGNETIC ATTITUDE MANEUVERS OF AN AXISYMMETRICAL SPINNING SATELLITE

A formulation used to determine the time-optimal geomagnetic attitude maneuvers subject to dynamic and geometric constraints is proposed in this paper. This was obtained by a direct search procedure based on a control function parametrization method, using linear programming to obtain numerical suboptimal solutions by linear perturbation. Due to its characteristics it can be used in small computers and to generate computer programs of general application. The dynamic modeling, the magnetic torque model and the suboptimal control procedure are presented. Simulation runs have verified the feasibility of the formulation thus derived and have shown a notable improvement in performance.

Multi-areas optimal reactive power flow

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area. The described method is successfully implemented and tested using the IEEE two area RTS 96 test system. Numerical results comparing the solutions obtained by the traditional and the proposed decentralized methods are presented for validation. ©2008 IEEE.